59,974 research outputs found
Reflection matrices for the vertex model
The graded reflection equation is investigated for the
vertex model. We have found four classes of diagonal
solutions and twelve classes of non-diagonal ones. The number of free
parameters for some solutions depends on the number of bosonic and fermionic
degrees of freedom considered.Comment: 30 page
An exterior for the G\"{o}del spacetime
We match the vacuum, stationary, cylindrically symmetric solution of
Einstein's field equations with , in a form recently given by Santos,
as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe.
There are three cases, depending on the radius of the cylinder. Closed timelike
curves are present in the exteriors of some of the solutions. There is a
considerable similarity between the spacetimes investigated here and those of
van Stockum referring to an infinite cylinder of rotating dust matched to
vacuum, with .Comment: 11 pages, LaTeX 2.09, no figures. Submitted to Classical and Quantum
Gravit
G\"{o}del-type universes in f(R) gravity
The gravity theories provide an alternative way to explain the current
cosmic acceleration without a dark energy matter component. If gravity is
governed by a theory a number of issues should be reexamined in this
framework, including the violation of causality problem on nonlocal scale. We
examine the question as to whether the gravity theories permit
space-times in which the causality is violated. We show that the field
equations of these gravity theories do not exclude solutions with
breakdown of causality for a physically well-motivated perfect-fluid matter
content. We demonstrate that every perfect-fluid G\"{o}del-type solution of a
generic gravity satisfying the condition is necessarily
isometric to the G\"odel geometry, and therefore presents violation of
causality. This result extends a theorem on G\"{o}del-type models, which has
been established in the context of general relativity. We also derive an
expression for the critical radius (beyond which the causality is
violated) for an arbitrary theory, making apparent that the violation of
causality depends on both the gravity theory and the matter content. As
an illustration, we concretely take a recent gravity theory that is free
from singularities of the Ricci scalar and is cosmologically viable, and show
that this theory accommodates noncausal as well as causal G\"odel-type
solutions.Comment: 7 pages, V3: Version to appear in Phys. Rev. D (2009), typos
corrected, the generality of our main results is emphasized. The illustrative
character of a particular theory is also made explici
Combining pot, atom and step economy (PASE) in organic synthesis. Synthesis of tetrahydropyran-4-ones
The combination of pot, atom and step economy (PASE) in the synthesis of organic molecules of medium complexity can lead to a significant 'greening' of a synthetic route. This is demonstrated by the synthesis of highly substituted tetrahydropyran-4-ones and is quantified by a series of recognised metrics, which demonstrate the efficiency of combining PASE over conventional synthetic strategies
Area Quantization in Quasi-Extreme Black Holes
We consider quasi-extreme Kerr and quasi-extreme Schwarzschild-de Sitter
black holes. From the known analytical expressions obtained for their
quasi-normal modes frequencies, we suggest an area quantization prescription
for those objects.Comment: Final version to appear in Mod. Phys. Lett.
Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic
generalization of the Knizhnik-Zamolodchikov equation is constructed. Via
Off-Shell Bethe ansatz an integrable representation for this equation is
obtained. It is shown that there exists a gauge transformation connecting this
equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on
torus.Comment: 20 pages latex, macro: tcilate
Interface States in Carbon Nanotube Junctions: Rolling up graphene
We study the origin of interface states in carbon nanotube intramolecular
junctions between achiral tubes. By applying the Born-von Karman boundary
condition to an interface between armchair- and zigzag-terminated graphene
layers, we are able to explain their number and energies. We show that these
interface states, costumarily attributed to the presence of topological
defects, are actually related to zigzag edge states, as those of graphene
zigzag nanoribbons. Spatial localization of interface states is seen to vary
greatly, and may extend appreciably into either side of the junction. Our
results give an alternative explanation to the unusual decay length measured
for interface states of semiconductor nanotube junctions, and could be further
tested by local probe spectroscopies
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